A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Gradient flows on distributions of distributions for machine learning tasks.
problem Designing gradient flows for datasets of probability distributions.
method Representing classes as conditional distributions, modeling datasets as mixture distributions, using Wasserstein over Wasserstein (WoW) distance and gradients.
result Demonstrated gradient flows for dataset transfer and distillation tasks.
NOFIS uses normalizing flows to estimate rare event probabilities more efficiently.
problem Accurate estimation of rare event probabilities using conventional methods is inefficient and resource-intensive.
method NOFIS learns a sequence of proposal distributions by minimizing KL divergence losses and estimates rare event probability using importance sampling.
result NOFIS outperforms baseline approaches in estimating rare event probabilities across 10 distinct test cases.
This paper studies gradient flows for sampling using various metrics and their affine invariance.
problem Sampling from probability distributions with unknown normalizations.
method Gradient flows in the space of probability measures, focusing on Kullback-Leibler divergence and affine invariance of metrics.
result Gradient flows of Kullback-Leibler divergence do not depend on the normalization constant, and affine invariance is achieved for certain metrics.
New gradient flows for non-negative and probability measures combining optimal transport and interaction forces.
problem Optimizing non-negative and probability measures using interaction forces and optimal transport.
method Interaction-Force Transport (IFT) gradient flows and their spherical variant, developed via infimal convolution of Wasserstein and spherical MMD tensors, with a particle-based optimization algorithm.
result The spherical IFT gradient flow provides global exponential convergence guarantees for both MMD and KL energy.
Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We consider in this work a specific family of cost metrics, namely \textit{tree me…
It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of prob…
Invertible flow-based generative models are an effective method for learning to generate samples, while allowing for tractable likelihood computation and inference. However, the invertibility requirement restricts models to have the same latent dimensionality as the inputs. This imposes significant architectural, memor…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expa…
This paper presents a methodology and numerical algorithms for constructing accelerated gradient flows on the space of probability distributions. In particular, we extend the recent variational formulation of accelerated gradient methods in (wibisono, et. al. 2016) from vector valued variables to probability distributi…
This paper proposes a new method to solve functional minimization problems in probability distributions using sliced-Wasserstein gradient flows.
problem Solving functional minimization problems in high-dimensional probability distributions is computationally challenging.
method The paper introduces a new approach using sliced-Wasserstein gradient flows to approximate the Jordan-Kinderlehrer-Otto (JKO) scheme, parameterizing densities with generative models.
result The proposed method is more flexible and computationally tractable compared to existing methods like JKO-ICNN.
We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and study its convergence properties. The MMD is an integral probability metric defined for a reproducing kernel Hilbert space (RKHS), and serves as a metric on probability measures for a sufficiently rich RKHS. We obtain conditions for conv…
Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to sample equilibrium states of strongly interacting many-body systems such as prote…
The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability density of the microscopical state is connected with a Perelman's functional of …
We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying space as a super Ricci flow as previously introduced by the second author. Our ma…
We investigate the probability of detecting combinatorial Morse flows on a simplicial complex via a random search. We prove that it is really small, in a quantifiable way.